Equivalence of the Derived Category of a Variety with a Singularity Category
By M. Umut Isik. 2010
107 citations recorded by the source corpus.
We prove an equivalence between the derived category of a variety and the equivariant/graded singularity category of a corresponding singular variety. The equivalence also holds at the dg level.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/9d29f9ce30fa2ae43bb01ee58bac33695ea801d4
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In Geometry and Topology
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- A geometric approach to Orlov’s theorem (2010, result): “View Y0 =W−1(0) as a C×-scheme via the action by scaling along the fibers of the projection Y → Z. Isik works with the C×-equivariant singularity category which is the Verdier quotient DSggr(Y0) = Db cohgr(Y0)/Perfgr(Y0).”
- Towards Mirror Symmetry for Varieties of General Type (2012, background): “.2 we have an equivalence5 (2.3) Db(S) ∼=Db(X,w,Zk) where Zk indicates a Zk-grading given by the (C∗)k-action on ˇw−1(0) induced from the split vector bundle. The hypersurface case is also treated in [Is10],[Sh11]. This equivalence is called renormalization flow in the physics literature. We assumed ”